The Moment in Kate Middleton's Cancer Announcement That Was Most 'Natural' and 'Accessible'

Kate Middleton's family was at the heart of her cancer announcement video.

There was a little wobble in her speech as the Princess of Wales, 42, mentioned her family — which "made it more natural and more accessible," royal biographer Sally Bedell Smith tells PEOPLE in a recent cover story.

Calling her cancer news a "huge shock," Kate said that she and Prince William "have been doing everything we can to process and manage this privately for the sake of our young family. As you can imagine, this has taken time."

Royal historian Amanda Foreman adds that following the controversy surrounding Kate's Mother's Day photo with Prince George, Princess Charlotte and Prince Louis, "Everyone had been worrying about the authenticity of the family and what the royal family represents. Not only were they being secretive — for which we now know why — and there was a fear that the seams were showing."

"What was so extraordinary was the incredible courage she showed in being herself. Which is why she is the most important member of the family --  because she is authentic at a moment of crisis for the family," she continues, adding that Princess Kate "chose to be as natural as possible — sitting on a bench in the garden."

The Princess of Wales spoke from the heart in the self-written address filmed in the garden of Windsor Castle, where she explained that she was undergoing "preventative chemotherapy" after tests following her abdominal surgery in January "found cancer had been present." Kate said that she and William took time to "explain everything to George, Charlotte and Louis in a way that is appropriate for them and to reassure them that I am going to be okay."

"As I have said to them: I am well and getting stronger every day by focusing on the things that will help me heal; in my mind, body and spirits," the royal mom said about how she is talking to her kids about her cancer treatment.

"The children are at the center of their world," a friend adds about Prince William, 41, and Princess Kate which was made clear in the royal's cancer announcement and the timing of it. The Princess of Wales waited to make the public announcement about her health until after her children were out of school for the Easter holiday. George, Charlotte and Louis aren't due back in the classroom until later in April, creating space for the family to spend private time together.

"You take heart from the extraordinary resilience of children," a longtime family friend adds.

Bedell Smith tells PEOPLE about Princess Kate’s video message, which sent shockwaves around the world on March 22, "We now understand the logic of the timing — waiting for the children to break up from school. And she struck a pitch-perfect note."

The Prince and Princess of Wales' family subsequently skipped the royal family’s church outing on Easter, breaking tradition from past years.

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As the Princess of Wales leans on Prince William during this time, she has a real partner in her husband. 

"He is a very reliable, strong person. She doesn’t feel isolated in this because of William, who is right beside her," a friend tells PEOPLE. 

"This is about supporting her and her feeling supported. It is a joint effort. She doesn’t feel isolated at all," the friend says. "The nuclear family that they have created so well is an immense support not only to him but to Catherine too."